Answer
domain of $F(x)$: $[1, 9]$
domain of $G(x)$: $[3, 10]$.
domain of $(F+G)(x)$: $[3, 9]$
domain of $F/G$: $[3, 9]$
Work Step by Step
The graph shows that $F(x)$ covers the x-values from $x=0$ to $x=9$. Thus, its domain is $[1, 9]$.
The graph shows that $G(x)$ covers the x-values from $x=3$ to $x=10$. Thus, its domain is $[3, 10]$.
The domain of $(F+G)(x)$ is the intersection (set of common elements) of the domain of $F$ and the domain of $G$.
Thus, the domain of $F+G$ is:
$$[1, 9] \cap [3, 10] = [3, 9]$$
The domain of $F/G$ is the intersection of the domain of $F$ and the domain of $G$ excluding the values of $x$ for which $G(x)=0$
Since there is no $x$ where $G(x) = 0$, then the domain of $F/G$ is:
$$[1, 9] \cap [3, 10] = [3, 9]$$
